Existence of solutions for some functional integrodifferential equations with nonlocal conditions

Munusamy, K.; Ravichandran, C.; Nisar, Kottakkaran Sooppy; Ghanbari, Behzad

doi:10.1002/mma.6698

Cited by 82 publications

(13 citation statements)

References 43 publications

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“…During the past decades, several mathematical models have been investigated to model prey-predator systems [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. The understanding of the relationship between herbivores and plants is extremely important in the behavior of the ecosystems.…”

Section: Introductionmentioning

confidence: 99%

A predator–prey model involving variable-order fractional differential equations with Mittag-Leffler kernel

et al. 2021

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This paper is about to formulate a design of predator–prey model with constant and time fractional variable order. The predator and prey act as agents in an ecosystem in this simulation. We focus on a time fractional order Atangana–Baleanu operator in the sense of Liouville–Caputo. Due to the nonlocality of the method, the predator–prey model is generated by using another FO derivative developed as a kernel based on the generalized Mittag-Leffler function. Two fractional-order systems are assumed, with and without delay. For the numerical solution of the models, we not only employ the Adams–Bashforth–Moulton method but also explore the existence and uniqueness of these schemes. We use the fixed point theorem which is useful in describing the existence of a new approach with a particular set of solutions. For the illustration, several numerical examples are added to the paper to show the effectiveness of the numerical method.

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Section: Introductionmentioning

confidence: 99%

A predator–prey model involving variable-order fractional differential equations with Mittag-Leffler kernel

et al. 2021

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“…(1.1) with the nonlinearity satisfying arbitrary-order polynomial growth condition, which makes the Sobolev compact embedding no longer valid and brings more difficulties for verifying the corresponding asymptotic compactness of the family of solutions semigroup {S ν (t)} t≥0 , ν ∈ [0, +∞). In the existing literature, many methods are not applicable to overcome these difficulties (see, e.g., [26][27][28][29][30][31][32]). In order to overcome the diffi-culty mentioned above, we introduce the asymptotic contractive function method to verify asymptotic compactness of a family of semigroups for autonomous dynamical systems (see Theorem 2.2) by referring to the methods and ideas in [2,3].…”

Section: Introductionmentioning

confidence: 99%

Upper semicontinuity of attractors for nonclassical diffusion equations with arbitrary polynomial growth

Xie

Zhu

2021

Adv Differ Equ

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In this paper, we mainly investigate upper semicontinuity and regularity of attractors for nonclassical diffusion equations with perturbed parameters ν and the nonlinear term f satisfying the polynomial growth of arbitrary order $p-1$ p − 1 ($p \geq 2$ p ≥ 2 ). We extend the asymptotic a priori estimate method (see (Wang et al. in Appl. Math. Comput. 240:51–61, 2014)) to verify asymptotic compactness and upper semicontinuity of a family of semigroups for autonomous dynamical systems (see Theorems 2.2 and 2.3). By using the new operator decomposition method, we construct asymptotic contractive function and obtain the upper semicontinuity for our problem, which generalizes the results obtained in (Wang et al. in Appl. Math. Comput. 240:51–61, 2014). In particular, the regularity of global attractors is obtained, which extends and improves some results in (Xie et al. in J. Funct. Spaces 2016:5340489, 2016; Xie et al. in Nonlinear Anal. 31:23–37, 2016).

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“…A variety of powerful methods have been used to study the nonlinear evolution equations, for the analytic and numerical solutions. Some of these methods, the Riccati Equation method [1], Hirota's bilinear operators [2], exponential rational function method [3], the Jacobi elliptic function expansion [4], the homogeneous balance method [5], the tanh-function expansion [6], first integral method [7,8], the subequation method [9], the expfunction method [10], the Backlund transformation, and similarity reduction [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29], are used to obtain the exact solutions of NLPDE.…”

Section: Introductionmentioning

confidence: 99%

Solitary Wave Solutions to the Multidimensional Landau–Lifshitz Equation

Neirameh

2021

Advances in Mathematical Physics

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In this paper, we study the different types of new soliton solutions to the Landau–Lifshitz equation with the aid of the auxiliary equation method. Then, we get some special soliton solutions for this equation. Without the Gilbert damping term, we present a travelling wave solution with a finite energy in the initial time. The parameters of the soliton envelope are obtained as a function of the dependent model coefficients.

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Existence of solutions for some functional integrodifferential equations with nonlocal conditions

Cited by 82 publications

References 43 publications

A predator–prey model involving variable-order fractional differential equations with Mittag-Leffler kernel

A predator–prey model involving variable-order fractional differential equations with Mittag-Leffler kernel

Upper semicontinuity of attractors for nonclassical diffusion equations with arbitrary polynomial growth

Solitary Wave Solutions to the Multidimensional Landau–Lifshitz Equation

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